Suppose A[1], A[2], A[3], ..., A[n] is a one-dimensional array and n > 50. (a) How many elements are in the array? (b) How many elements are in the following subarray? A[4], A[5], ..., A[33] 30 (c) If 3 s ms n, what is the probability that a randomly chosen array element is in the following subarray? A[3], A[4], ..., A[m] (m-2) (d) What is the probability that a randomly chosen array element is in the subarray shown below if n = 57? A[[n/2]], A[[n/2] + 1], ..., A[n] 30 57
Suppose A[1], A[2], A[3], ..., A[n] is a one-dimensional array and n > 50. (a) How many elements are in the array? (b) How many elements are in the following subarray? A[4], A[5], ..., A[33] 30 (c) If 3 s ms n, what is the probability that a randomly chosen array element is in the following subarray? A[3], A[4], ..., A[m] (m-2) (d) What is the probability that a randomly chosen array element is in the subarray shown below if n = 57? A[[n/2]], A[[n/2] + 1], ..., A[n] 30 57
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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How did they get the answer?
![**Title: Understanding Arrays and Subarrays**
**Introduction:**
Suppose \( A[1], A[2], A[3], \ldots, A[n] \) is a one-dimensional array, and \( n > 50 \).
---
**(a) Determining the Total Number of Elements in the Array**
- **Question:** How many elements are in the array?
- **Answer:** \( n \)
The number of elements in a one-dimensional array is given as \( n \).
---
**(b) Counting Elements in a Specific Subarray**
- **Question:** How many elements are in the subarray \( A[4], A[5], \ldots, A[33] \)?
- **Answer:** 30
To find the number of elements, subtract the starting index from the ending index and add 1. Therefore, \( 33 - 4 + 1 = 30 \) elements.
---
**(c) Calculating the Probability of a Random Element Belonging to a Subarray**
- **Condition:** \( 3 \leq m \leq n \)
- **Question:** What is the probability that a randomly chosen array element is in the subarray \( A[3], A[4], \ldots, A[m] \)?
- **Answer:** \( \frac{m - 2}{n} \)
The probability is calculated by taking the number of elements in the subarray (from index 3 to \( m \)) which is \( m - 2 + 1 \) and dividing by the total number of elements, \( n \).
---
**(d) Probability of an Element in Another Specific Subarray**
- **Question:** What is the probability that a randomly chosen array element is in the subarray \( A[\lceil n/2 \rceil], A[\lceil n/2 \rceil + 1], \ldots, A[n] \) if \( n = 57 \)?
- **Answer:** \( \frac{30}{57} \)
To find the subarray start, compute \( \lceil 57/2 \rceil = 29 \). The number of elements is from index 29 to 57, which is \( 57 - 29 + 1 = 29 \). The probability is then \( \frac{29}{57} \).
---
**Conclusion:**
In this exercise,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8326e22a-74be-4cd9-ae2c-0a0d10569242%2Fa7d8137c-8f46-4986-be04-51ae9c7f750e%2Frcvv6wc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Arrays and Subarrays**
**Introduction:**
Suppose \( A[1], A[2], A[3], \ldots, A[n] \) is a one-dimensional array, and \( n > 50 \).
---
**(a) Determining the Total Number of Elements in the Array**
- **Question:** How many elements are in the array?
- **Answer:** \( n \)
The number of elements in a one-dimensional array is given as \( n \).
---
**(b) Counting Elements in a Specific Subarray**
- **Question:** How many elements are in the subarray \( A[4], A[5], \ldots, A[33] \)?
- **Answer:** 30
To find the number of elements, subtract the starting index from the ending index and add 1. Therefore, \( 33 - 4 + 1 = 30 \) elements.
---
**(c) Calculating the Probability of a Random Element Belonging to a Subarray**
- **Condition:** \( 3 \leq m \leq n \)
- **Question:** What is the probability that a randomly chosen array element is in the subarray \( A[3], A[4], \ldots, A[m] \)?
- **Answer:** \( \frac{m - 2}{n} \)
The probability is calculated by taking the number of elements in the subarray (from index 3 to \( m \)) which is \( m - 2 + 1 \) and dividing by the total number of elements, \( n \).
---
**(d) Probability of an Element in Another Specific Subarray**
- **Question:** What is the probability that a randomly chosen array element is in the subarray \( A[\lceil n/2 \rceil], A[\lceil n/2 \rceil + 1], \ldots, A[n] \) if \( n = 57 \)?
- **Answer:** \( \frac{30}{57} \)
To find the subarray start, compute \( \lceil 57/2 \rceil = 29 \). The number of elements is from index 29 to 57, which is \( 57 - 29 + 1 = 29 \). The probability is then \( \frac{29}{57} \).
---
**Conclusion:**
In this exercise,
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